Compound Poisson approximation for simple transient random walks in random sceneries

2022/12/19 by Chenavier, Nicolas, Darwiche, Ahmad, Rousselle, Arnaud
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2212.09395

Abstract

Given a simple transient random walk (S_n)_{n≥ 0} in Z and a stationary sequence of real random variables (ξ(s))_{s∈ Z}, we investigate the extremes of the sequence (ξ(S_n))_{n≥ 0}. Under suitable conditions, we make explicit the extremal index and show that the point process of exceedances converges to a compound Poisson point process. We give two examples for which the cluster size distribution can be made explicit.

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